CCML Video Contest – Meet 3 2016-2017
The CCML is pleased to announce the CCML Video Contest for the 2016 − 2017 season. Each half (freshman/sophomore or
junior/senior) of your team can submit up to two video solutions to the problems below.
Judging
The video submissions can earn your team points toward your overall total on contest day. Here are the guidelines:

Students from each half of your team (freshman/sophomore or junior/senior) from your school may submit up to two videos
on the given problem. Each video submitted must be produced by different students, but must all be from the appropriate
grade band. If your school decides to submit two f/s videos, there should be different students in each video.

Each video should be no more than FOUR minutes in length for the f/s problem, and no more than SIX minutes in length for
the j/s problem.

The problems are to be solved and the videos produced by student groups. The bulk of the work should be done by students.
A parent or teacher holding a camera is fine, but solving a problem for the students is not.

Videos must be produced by a group of at least two students, and at most five students. Each participating student’s
contribution should be made evident either from an appearance in the video or a credit at the beginning or end of the video.
Indicate names of all students involved (maximum of 5) in credits or introductions at the beginning or end of the video.

Points will be awarded as follows.
o

Videos will be ranked by correctness of solution, thoroughness of explanation, and creativity. You do not have to
prove everything that you say, but justification of big ideas is important when possible. The top videos will earn 5,
4, 3, 2, or 1 points each, respectively, for placing in the top five.
Creative solutions and presentations are encouraged, but correct math trumps all. Please make the focus of your video the
mathematics. If you have a creative context, great, but it should not be the focus of your video. Soundtracks should not
distract or interfere with the explanation of the solution.
Submission

Coaches should select the best two videos for each grade level to submit for judging.

Coaches should upload videos to Google drive and share access with Michael Caines ([email protected]). Please use the
following naming conventions for the videos: school_level_teamnumber_contestnumber_year. For example, a submission
for CCML 3 for a f/s team from Kelly in the 2015−2016 school year should be named as follows,
kelly_fs_team1_contest3_1516. A submission from a j/s team from Lakeview should be named
lakeview_js_team1_contest3_1516

All submissions must be shared by 5pm on Tuesday, January 17, 2017.
Please direct any questions about the contest to Michael Caines ([email protected]). Coaches who are interested in helping judge the
submissions should email Michael Caines by the submission deadline.
Problems:

Freshman/Sophomore Problem:
(a) How many diagonals does a regular decagon have?
(b) If two diagonals of a regular decagon are chosen at random, what is the probability that they are parallel?
(c) If three vertices of a regular decagon are chosen at random, what is the probability that they determine a right
triangle?

Junior/Senior Problem:
In the following problems, < x, y > denotes a two-dimensional vector with x, y 
(a) Let f   x, y   
  x,  y
1
x2  y 2
.
and g   x, y    x,  y . (Note that the inputs and outputs of these functions
are both vectors.) Determine the solution set of f   x, y    g   x, y   .
(b) Determine any fixed points of g.
(c) Determine any fixed points of f.
(d) Let h   x, y    x 2  y 2 , 2 xy . Determine any fixed points of h.